Tail end structure for an aircraft fuselage

ABSTRACT

The tail end structure of an aircraft has a cross-sectional configuration th laterally and downwardly extending lobes reaching outside a circular cross-section tail end structure, yet staying within the silhouette of the circular cross-section tail end structure as viewed from the top, the side, and the bottom, whereby the boundary layer formation and the boundary layer separation are improved as compared to a tail end structure having the circular cross-section.

FIELD OF THE INVENTION

The invention relates to a tail end structure for the fuselage of anaircraft having a raised cross-sectional configuration deviating from acircular cross-section.

DESCRIPTION OF THE PRIOR ART

Tail end structures of this type are known, for example, from GermanPat. No. 674,433 (Schroeder) and from U.S. Pat. No. 3,955,781 (Tupolevet al). It is also known to provide the tail end structure with acircular cross-section as, for example, in the well known airbus.

German Pat. No. 674,433 discloses a fuselage configuration having asomewhat oval upper cross-sectional configuration and a flattened lowercross-sectional configuration. The fuselage itself is made of corrugatedmetal which is surrounded by a fabric or webbing secured to the ridgesformed by the corrugations and covering the valleys between the ridges.A particular tail end construction is not disclosed in German Pat. No.674,433.

U.S. Pat. No. 3,955,781 (Tupolev et al) discloses a delta wingedaircraft with a fuselage having two portions. Each portion forms part ofa circular cross-section, whereby the upper portion has a smaller radiusand the lower portion has a substantially larger radius so as to flattenthe bottom of the fuselage. A specific tail end construction is notdisclosed in Tupolev et al. There is room for improvement with regard tothe tail end construction, especially with regard to providing betterflow conditions for the air flow along the tail end structure.

OBJECTS OF THE INVENTION

In view of the foregoing it is the aim of the invention to achieve thefollowing objects singly or in combination:

to construct the tail end of an aircraft or spacecraft fuselage in sucha manner that improved conditions are provided for the boundary layerformation, especially along the tail end underside and for the boundarylayer separation;

to construct the tail end in such a way that drag is reduced as comparedto the prior art, especially in comparison with tail end structureshaving circular cross-sections; and

to modify the cross-sectional area of the tail end structure withoutmodifying its silhouette as viewed from the side, from the top, and fromthe bottom as compared to the silhouette of a conventional tail endstructure having a circular cross-section.

SUMMARY OF THE INVENTION

According to the invention there is provided a tail end structure forthe fuselage of an aircraft or spacecraft having cross-sections with acentroid displaced downwardly relative to the centroid of a circularcross-section. This downward displacement of the cross-sectionalcentroid is achieved by downwardly and laterally extending lobes whichare so sized that the lower, upper, and lateral boundary or silhouettecontours remain unchanged within the silhouette of a tail end structurehaving a circular cross-section.

BRIEF DESCRIPTION OF THE DRAWINGS

In order that the invention may be clearly understood, it will now bedescribed, by way of example, with reference to the accompanyingdrawings, wherein:

FIG. 1 is a schematic, symbolic illustration of the silhouette of anaircraft fuselage including the tail end structure located in arectangular coordinate system, whereby the three sectional views aretaken along section plane A--A, but through three different tail endstructures to illustrate a conventional circular cross-section and twocross-sections through tail end structures according to the invention;

FIG. 2 is also a view against the section plane A--A, but on an enlargedscale as compared to FIG. 1, and illustrating in a superposed view therelationship between the circular conventional cross-sectionalconfiguration (V0) and the modified cross-sectional configurations (V2,V3) according to the invention;

FIG. 2a shows the circular cross-sectional configuration (V0) of aconventional tail end structure providing a reference plane for definingthe invention;

FIG. 2b is a cross-sectional view of a tail end structure (V2) accordingto the invention;

FIG. 2c is another cross-sectional view of a tail end structure (V3)according to the invention;

FIG. 3 is a diagram showing the relationship of the curvature radii, ofthe centers of curvature spacings, of the circumference ratios, as wellas the area ratios, all shown as a function of a tail end deformationfactor ξ which is a dimensionless number ranging from zero, at theinterface between the tail end structure and the fuselage, to one at thetail end;

FIG. 4 is a view from right to left in FIG. 1 against the tail end ofthe fuselage of the aircraft for showing the panel models for theright-hand half of the fuselage for a conventional tail end structure(V0) with a circular cross-section and for two embodiments (V2 and V3)of the invention;

FIG. 5a shows the frictionless flow lines and the boundary wall flowlines for a conventional tail end structure (V0);

FIGS. 5b and 5c are views similar to that of FIG. 5a, however, showingthe frictionless flow lines and the boundary wall flow lines for theembodiments (V2 and V3) according to the invention;

FIG. 6 illustrates sectional views in section line A--A at x1=0.75 inFIG. 1, showing on the left-hand side of each section the boundary layerthickness (δ) and on the right-hand portion of each section the boundarylayer displacement thickness (δ1) of a conventional tail end section(V0) and of the two tail end sections (V2, V3) according to theinvention;

FIG. 7 are views corresponding to those of FIG. 6, however, showing thesections at the section plane B--B at x1=0.89 in FIG. 1;

FIG. 8a shows boundary layer separation configurations for aconventional tail section with a circular cross-section; and

FIG. 8b shows the boundary layer separation configurations of oneembodiment (V3) of the tail section according to the inventionillustrating the displacement of the separation bubble toward the tailend.

DETAILED DESCRIPTION OF PREFERRED EXAMPLE EMBODIMENTS AND OF THE BESTMODE OF THE INVENTION

FIG. 1 illustrates symbolically an aircraft fuselage in a rectangularcoordinate system wherein the ordinate is x3' and the abscissa is x1'.The ordinate and abscissa are indicated in meters. A relative scale x1indicates the total length Lref=1 of the fuselage. The length of thefront part and of the cylindrical part of the fuselage together isindicated by C2. The circular cross-section V0 shown in FIG. 1 relatesto a conventional tail end structure having this circular cross-sectionthroughout its length Lref-C2. The tail end structures of the inventionV2 and V3 do not have such a circular cross-section. However, thecircular cross-section is used as a reference plane for comparing thecross-sections V2 and V3 according to the invention with the prior artV0.

FIG. 1 further shows a relative scale ξ ranging from zero to 1. ξ iszero at the interface V--V where the tail section merges into thecylindrical part of the fuselage. ξ is one at the very end of the tailstructure. The factor ξ represents the degree of deformation of the tailend structure according to the invention and is related to the x1'coordinate as follows:

    ξ=C1(x1'-C2),

wherein C2 is as defined above, and C1=1/(Lref-C2).

FIGS. 2, 2a, 2b, and 2c show a schematic cross-section of the tail endstructures V2 and V3 according to the invention against the backdrop ofthe circular conventional cross-section V0 forming a reference planeseparately shown in FIG. 2a. It may be assumed that the section of FIG.2 is taken, for example, in the plane ξ=0.65. The contour or silhouetteboundaries for the conventional circular cross-section are provided bythe top boundary line T, by the lateral boundary lines K3, and by thebottom boundary line U. Thus, in the plane of FIG. 1, the silhouette orcontour of the conventional circular cross-section is the same as viewedfrom all four directions. The cross-sections V2 and V3 according to theinvention deviate from the circular cross-section as shown, however, insuch a way, that the tail end structures according to the inventionremain within the contour or silhouette of the circular tail endstructure V0. This is so even though the tail end structure V2 haslateral boundary lines K2 which are vertically aligned below the lateralboundary lines K3. The circular cross-section of the conventional tailend structure V0 has a first centroid or surface center of gravity S1located at the center of the circular cross-section having the radiusro. According to the invention the cross-sectional surfaces of theembodiments V2 and V3 have a second centroid S2 located below the firstcentroid S1 by a spacing a1 that will depend on the particularcross-sectional surface involved. Both centroids S1 and S2 are locatedon a central vertical line VL.

The cross-section V2 separately shown in FIG. 2b, according to theinvention, has two laterally and downwardly extending first lobes W2 andan upwardly and centrally located lobe W2'. The first lobes W2 aremirror-symmetrically arranged relative to the vertical line or plane VL.All the lobes W2 and W2' have the same radius r1 of curvature having alength as given below. Each lobe W2 and W2' has a different center ofcurvature CC1, CC2, and CC3. The centers of curvature CC1 and CC2 arelocated on their respective lobe line LL passing through the firstcentroid S1 and extending at an angle α of, for example, 45° relative tothe vertical line VL. The angle α is within the range of 35° to 55°preferably within the range of 40° to 50°. Additionally, the centers CC1and CC2 are spaced from the first centroid S1 by a spacing a2. Thecenter of curvature CC3 for the upper central lobe W2' is located on thevertical line VL vertically above the first centroid S1 and spaced fromthe first centroid S1 by the above mentioned spacing a1. The angularextent of the upper lobe W2' corresponds to 180°-2×β as shown, whereby βcorresponds, for example, to 26.565°, however β may be within the rangeof 20° to 30°. The angular extent of the two lower lobes W2 correspondsto 90°+β as shown, whereby the 90° are measured between a vertical lineextending through the respective center of curvature CC1 or CC2 inparallel to the central vertical line VL, and a horizontal lineextending through both centers of curvature CC1 and CC2, as well asthrough the second centroid S2. The angle β is measured against thishorizontal line as shown.

The second embodiment V3 separately shown in FIG. 2c, according to theinvention, has an upper portion forming a semi-circle coinciding withthe upper part of the circular cross-section V0 of the prior art.However, the lower portion of the cross-section V3 has two laterally anddownwardly extending lobes W3 with a radius of curvature r3 having itsorigin in respective curvature centers CC4 and CC5 located on the abovementioned lobe lines LL and spaced from the first centroid S1 by thespacing a3. The angular extent of the lobes W3 is approximately 90° asshown.

The cross-sections blend smoothly from the circular shape at ξ=0 intoshapes like V2 or V3 (FIGS. 2b and 2c) at the end of the fuselage ξ=1(for the relations of r1, r2, r3, a1, a2, and a3, see below).

FIG. 3 shows the dimensional relationship of the above mentioneddistances a1, a2, and a3 in meters as a function of the tail enddeformation factor ξ. FIG. 3 further shows the dimensional relationshipof the above mentioned radii ro, r1, and r2 also as a function of thedeformation factor in meters or fractions thereof. FIG. 3 shows thesurface ratios (F_(V2) /Fo) and (F_(V3) /Fo) and the circumferentialratios (U_(V2) /Uo) and (U_(V3) /Uo) of the cross-sections V2 and V3according to the invention compared to the surface Fo and thecircumference Uo of the conventional circular cross-section. Therespective conventional ratios are equal to one. The present ratiosbecome larger than one toward the tail end, except that the surfaceratio (F_(V2) /Fo) becomes slightly less than 1 toward the very tail endwhere ξ=1.

According to the invention, the following empirical relationships areestablished between the circle radius ro and ξ on the one hand, and thedistance a1, a2, a3, and r1, r2 on the other hand. ##EQU1##

FIG. 3 illustrates the above relationships. It will also be seen fromFIG. 3 that the surface area ratio (F_(V2) /Fo) and the circumferentialratio (U_(V2) /Uo) of the embodiment V2 according to the invention arequite close to one as mentioned above so that these ratios indicate thatthe embodiment V2 has substantially the same flow exposed surface areaand substantially the same volume in the tail section as theconventional tail section V0. However, the different shape V2 improvesthe flow conditions. The respective surface ratio (F_(V3) /Fo) and thecircumferential ratio (U_(V3) /Uo) of the embodiment V3 shows that thevolume and the flow exposed area are larger than in the conventionalcross-section V0, and provides improved flow conditions.

The left-hand part of FIG. 4 illustrates the so-called panel models forthe conventional tail section V0. Panel models for the tail sections V2and V3 according to the invention are shown in the center and at right.

FIG. 5a shows by full lines the computed frictionless flow lines of theprior art tail end structure V0. Dashed lines show the boundary wallflow lines. These lines are drawn in the coordinate plane xα with the x1and x2, whereby xα is a common reference plane. On the upper side thefrictionless flow for the Vo structure is most divergent. FIGS. 5b and5c show the respective lines for a tail end structure V2 and V3according to the invention respectively. It is noted that on the upperside of the embodiment V3 the least divergence takes place. Theconvergence on the other hand is the least on the lower side of theembodiment V2. However, for the boundary layer characteristic, a bend inthe flow lines is controlling. This bend is signified for the prior arttail end V0 by a strong convergence of all the boundary wall flow lineson the lower or rather underside of the fuselage. On the other hand, theboundary wall flow lines for the embodiment V2 and V3 extendsubstantially in parallel to the underside of the fuselage and in FIG.5c these boundary wall flow lines even have a somewhat convergenttendency, please see the upper right-hand corner of FIG. 5c.

These features of the embodiments V2 and V3 result in improved boundarylayer characteristics including a substantially reduced drag and hencean improved efficiency with regard to speed and fuel consumption.

FIGS. 6 and 7 provide further information regarding the boundary layerseparation characteristics, whereby FIG. 6 reflects sectional views onthe section line A--A in FIG. 1, where x1=0.75 (about), whereas FIG. 7illustrates views along section plane B--B in FIG. 1, where x1=0.89(about). In all instances the left-hand part of each illustration showsthe boundary layer thickness δ while the right-hand part of eachillustration shows the boundary layer displacement thickness δ1. It willbe noted that in all instances V0, V2 and V3 in the sectional plane A--Acorresponding to x1=0.75 the entire flow is convergent at the lower lineof symmetry. As a result, the boundary layer thickness increases towardthe tail end on the underside of the fuselage, please see FIG. 6.However, the thickening is less in the embodiments V2 and V3 of theinvention. Further, the boundary layer thickness distribution changessubstantially at the section plane B--B corresponding to x1=0.89 asshown in FIG. 7. In the illustration for the prior art tail end V0 asubstantial thickening takes place while in the embodiments V2 and V3 ofthe invention merely a small lobe is formed in the boundary layerthickness contour adjacent to the lower plane of symmetry.

FIG. 6 shows that the boundary layer is thicker on the bottom of thetail end section of the fuselage than on its upper side. The ratio ofthe boundary layer thickness to the boundary layer displacementthickness (δ/δ1) is in the same order of magnitude as the respectiveratio of the two-dimensional reference plane also known as the1/7--power-boundary layer. In the conventional construction V0 theboundary layer at the lower surface of the tail end section, at x1=0.75,is about 10% thicker than in the embodiments V2 and V3 according to theinvention. At the lower contour line the boundary layer thickness at thecross-section B--B (x1=0.89) as shown in FIG. 7, goes down from about8.5 for V0 to about 2 for V2 and V3. At the tail end cross-sectionlocated at the leading edge of the elevator assembly there is a lobe inthe boundary layer thickness contour in the prior art tail section V0.Such a lobe indicates a possible longitudinal vortex type boundary layerseparation. However, toward the lower line of symmetry where x2 is equalto 0.5, the separation changes into a form indicating a two-dimensionalseparation, possibly a dead-water type of separation. The situation isdifferent in the embodiment V2 and V3 where the boundary layer thicknesscontour has such a lobe that only one longitudinal vortex typeseparation is indicated without any separation near the lower line ofsymmetry.

With regard to the wall shearing stress distributions it is noted thatin the prior art structure V0 a substantial drop is noted at the lowersymmetry plane, whereas in the embodiment V3 a much smootherconfiguration is noted.

Regarding the possible boundary layer separation characteristics it isnoted that in the prior art structure V0 at x1=0.9, a closed separationbubble is formed which extends along the underside of the tail endsection. FIG. 8a shows in this respect the lobe formation of thethickness contour together with the convergence of the boundary wallflow lines providing the possibility of an embedded vortex typelongitudinal separation to the left and right of the line of symmetry.

FIG. 8b shows for the embodiment V3 at x1=0.9 a longitudinal vortex typeseparation alone. The separation bubble is shifted further down towardthe end of a tail end section. Stated differently, the boundary layer atthe under surface of the structure V2 or V3 is not in danger ofseparation contrary to the prior art structure V0.

Locating the second centroid S2 below the conventional location at S1 bymodifying the cross-sectional configuration to V2 or V3 results in amore advantageous boundary layer characteristic, especially at the lowersurface of the tail end section in the embodiments V2 and V3 as comparedto the conventional structure V0. Further, the structures V2 and V3according to the invention are just as simple to manufacture as a tailsection having a circular cross-section because the increase in thevolume and surface do not pose any problems. The separationcharacteristics and the drag characteristics are also impoved. The wingand the raised tail end structure guide in the same manner thefrictionless flow and thus the boundary layer under the tail endsection. Further, the on-flow to the elevator assembly near the fuselageis improved.

LIST OF SYMBOLS

Fo=frame sectional surface of conventional tail section V0 having acircular cross-section.

F_(V2) ; F_(V3) =frame sectional surface of tail sections V2 and V3according to the invention.

(F_(V2) /Fo); (F_(V3) /Fo)=surface ratios comparing tail sectionsurfaces of the invention with conventional tail section Fo having acircular cross-section.

Uo=circumference of conventional tail section V0 having a circularcross-section.

U_(V2) ; U_(V3) =circumference of tail sections V2 and V3 according tothe invention.

(U_(V2) /Uo); (U_(V3) /Uo)=circumferential ratios comparing tail sectioncircumferences of the invention with conventional tail section V0 havinga circular cross-section.

K2=lateral contour boundary of embodiment V2.

K3=lateral contour boundary of embodiment V3.

T=upper contour boundary line.

U=lower contour boundary line.

W2=lower lateral lobes (first lobes) of embodiment V2.

W2'=upper central lobe (second lobe) of embodiment V2.

W3=lower lateral lobes (first lobes) of embodiment V3.

V0=cross-section through a conventional cylindrical tail structureproviding a reference plane.

V2=cross-section through a first tail end structure according to theinvention.

V3=cross-section through a second tail end structure according to theinvention.

a1=spacing above first centroid S1 for defining center CC3 of curvatureof a first lobe radius r2.

a2=spacing laterally below first centroid S1 for defining centers CC2,CC3 of curvature for first lobe radius r2.

a3=spacing laterally below first centroid S1 for defining centers CC4and CC5 of curvature for second lobe radius r3.

Lref=length of fuselage from nose tip to the end of the tail section.

C1=(1/Lref-C2).

C2=length of fuselage section including nose portion and cylindricalportion C1+C2=Lref.

ro=radius of circular conventional section V0.

r1=first lobe radius of first tail cross-section V2 of invention, about0.7×ro.

r2=second lobe radius of second tail cross-section V3 of invention,about 0.25×ro at the tail end for ξ=1.

x1=first surface coordinate for sectional plane.

x2=second surface coordinate for sectional plane.

xα=reference plane for x1 or x2.

x1'=rectangular reference coordinates.

x2'=rectangular reference coordinates.

x3'=rectangular reference coordinates, a dimensionless number.

ξ=tail end coordinate.

δ=boundary layer thickness.

δ1=boundary layer displacement thickness.

α=lobe line angle, within range of about 35° to 55°.

β=lobe limit angle, of about 26.565°.

S1=first surface center of gravity or centroid of circular sectionalplane V0.

S2=second surface center of gravity or centroid of sectional planesthrough tail sections V2 and V3 of the invention.

Although the invention has been described with reference to specificexample embodiments, it will be appreciated, that it is intended tocover all modifications and equivalents within the scope of the appendedclaims.

What I claim is:
 1. A tail end structure for an aircraft fuselage havinga longitudinal central axis extending centrally through said fuselage,comprising a circular sectional reference plane as defined by a circularfuselage and extending through an interface between said circularfuselage and said tail end structure perpendicularly to saidlongitudinal central axis, said circular reference plane having a firstcentroid, said tail end structure further comprising a tailcross-section with an upper cross-sectional portion within said circularsectional plane above said first centroid and a lower cross-sectionalportion below said first centroid, said lower cross-sectional portionhaving two first lobes extending laterally and downwardly outside saidcircular sectional reference plane, said lower cross-sectional portionhaving a second centroid in said tail cross-section located under saidfirst centroid so that a vertical line passes through both centroids,said tail cross-section having upper, lower and lateral contour orsilhouette boundary lines appearing within a silhouette formed by saidcircular sectional reference plane, so that the projection or silhouetteof the tail end structure as viewed from the side and from above orbelow remains the same as that of a tail end structure having across-section corresponding to that of said circular sectional referenceplane, whereby said cross-sectional portions of said tail end structureblend smoothly into said circular fuselage.
 2. The tail end structure ofclaim 1, wherein said first and second centroids are located on acentral vertical line (VL) passing longitudinally through said centralaxis and through said first and second centroids.
 3. The tail endstructure of claim 2, wherein said tail cross-section (V2) has an uppercross-sectional portion with second central upper lobe (W2') having anupper tip (T) coinciding with a point on a circle defining said circularsectional reference plane (V0), said second upper lobe (W2') having acenter of curvature (CC3) located on said central vertical line (VL),and wherein said first lobes (W2) extending laterally and downwardly andsaid second upper lobe (W2') have the same radius (r1) of curvature,said first lobes (W2) having different centers of curvature (CC1; CC2).4. The tail end structure of claim 3, wherein, in said tailcross-section (V2), said different centers of curvature (CC1; CC2) ofsaid first laterally and downwardly extending lobes (W2) are located onrespective radial lobe lines (LL) extending at an angle (α) relative tosaid central vertical line (VL) passing through said first and secondcentroids, said centers of curvature (CC1; CC2) being spaced from saidfirst centroid (S1) on said respective radial lobe line (LL) by aspacing a2, and wherein said center of curvature (CC3) of said secondcentral upper lobe (W2') is spaced above said first centroid by aspacing a1, said spacings a1 and a2 being proportional to a tail enddeformation factor ξ, (FIG. 3).
 5. The tail end structure of claim 4,wherein said angle (α) is within the range of 35° to 55°, preferablywithin the range of 40° to 50°.
 6. The tail end structure of claim 4,wherein, in said tail cross-section (V2), said first laterally anddownwardly extending lobes (W2) have an angular limit defined by 90°plus an angle (β) measured in the respective center of curvature (CC1;CC2), and wherein said second upwardly extending lobe (W2') has anangular limit of 180° minus 2β measured in the respective center ofcurvature (CC3) of said upwardly extending lobe (W2').
 7. The tail endstructure of claim 6, wherein β is within the range of 20° to 30°,preferably 26.565°.
 8. The tail end structure of claim 3, wherein saidcenter of curvature (CC3) of said second central upper lobe (W2') andsaid first and second centroids are located on said central verticalline (VL), and wherein said center of curvature (CC3) is spaced abovesaid first centroid (S1) by a distance a1 which corresponds to thevertical spacing between the first and second centroids.
 9. The tail endstructure of claim 3, wherein said centers of curvature (CC1; CC2) ofsaid first lobes (W2) are located on a common horizontal line alsopassing through said second centroid (S2).
 10. The tail end structure ofclaim 3, wherein said radius r1 of curvature of said lobes (W2 and W2')corresponds to about: r1≈0.75×ro, wherein ro is the radius of saidcircular sectional reference plane (V0).
 11. The tail end structure ofclaim 3, wherein said spacing a1 of said center of curvature (CC3) abovesaid first centroid corresponds to about: a1≈0.25×ro, wherein ro is theradius of said circular sectional reference plane (V0).
 12. The tail endstructure of claim 2, wherein said tail cross-section (V3) has two firstlobes (W3) arranged mirror-symmetrically relative to said centralvertical line (VL) to form a configuration (V3) having a lobe radius r2with a center of curvature (CC4; CC5) located on a lobe line (LL)extending downwardly through said first centroid (S1) at a lobe lineangle (α) relative to said central vertical line (VL) for forming saidfirst lobes (W3).
 13. The tail end structure of claim 12, wherein, insaid tail cross-section (V3), said lobe radius r2 of said first lobes(W3) satisfies r2=0.25×ro at the tail end where a tail sectiondeformation factor ξ equals 1, wherein ro is the radius of said circularsectional reference plane, and wherein said lobe line angle α is withinthe range of about 35° to about 55°, preferably 40° to 50°.
 14. The tailend structure of claim 12, wherein said upper cross-sectional portion ofsaid tail cross-section (V3) has the shape of a semi-circle coincidingwith an upper half of said circular sectional reference plane (V0)having a radius (ro), and wherein said first lobes (W3) extendinglaterally and downwardly both have the same radius r2 of curvature anddifferent centers of curvature (CC4; CC5).
 15. The tail end structure ofclaim 14, wherein said different centers of curvature (CC4; CC5) of saidfirst laterally and downwardly extending lobes (W3) are located onrespective radial lobe lines (LL) extending at said angle (α) relativeto said central vertical line (VL) passing through said first and secondcentroids, said centers of curvature (CC4; CC5) being spaced on therespective radial lobe line (LL) from said first centroid (S1) by aspacing a3, and wherein said upper cross-sectional portion having saidsemicircle has a center of curvature coinciding with said first centroid(S1), said spacing a3 being proportional to a tail end deformationfactor ξ, (FIG. 3).
 16. The tail end structure of claim 15, wherein saidfirst laterally and downwardly extending lobes (W3) have an angularlimit of 90° relative to the respective center of curvature (CC4; CC5),and wherein said upper cross-sectional portion has an angular limit of180° relative to said first centroid (S1).
 17. The tail end structure ofclaim 15, wherein said spacing a3 is a function of said tail enddeformation factor ξ as follows:

    a3=3/4√2roξ,

wherein ro is the radius of said circular sectional reference plane(V0), and wherein ξ is

    ξ=C1(x1'-C2),

wherein C1 is the inverse of length of the tail end structure between acylindrical fuselage section and the tail end, wherein x1' is therectangular coordinate in the direction of said central axis, wherein C2is the length of the aircraft fuselage from nose tip to beginning of thetail end structure, and wherein said radius of curvature r2 is afunction of said tail end deformation coordinate ξ as follows:

    r2=ro(1=3/4ξ),

whereby r2=0.25×ro for ξ=1.
 18. The tail end structure of claim 12,wherein, in said tail cross-section (V3), said first lobes (W3) have acontinuous smooth transition for said length (C1) in accordance withsaid equations for a3 and r2.